The Bell-Weibull cure rate survival model: modeling, properties, inference and local influence

• Grant number: 18/04938-7
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: May 01, 2018
• End date: April 30, 2019
• Field of knowledge: Physical Sciences and Mathematics - Probability and Statistics - Applied Probability and Statistics
• Principal Investigator: Adriano Kamimura Suzuki
• Grantee: Carlos Miguel Toste Sisto
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

In this work we propose a new long-term survival model called Bell-Weibull with cure fraction (BWcr). Considering that the event of interest can be caused by M different latent risk factors, this new parametric model will be obtained by assuming that M follows a Bell distribution and the activation time of the jth factor follows a Weibull distribution. In addition to its construction and properties, we will conduct for inferential purpose a Bayesian approach using Monte Carlo Markov Chain (MCMC) methods. With the objective of to detect influential observations in the data we will consider a Bayesian case deletion influence diagnostics based on the psi-divergence. We will show its applicability to artificial and real data sets. All computational implementations will be performed using the JAGS and R systems. (AU)